Projective representation

Summary

In the field of representation theory in mathematics, a projective representation of a group $G$ on a vector space $V$ over a field $F$ is a group homomorphism from $G$ to the projective linear group

$$\mathrm{PGL}(V) = \mathrm{GL}(V) / F^*,$$

where GL(V) is the general linear group of invertible linear transformations of $V$ over $F$, and $F^{\ast}$ is the normal subgroup of $\mathrm{GL}(V)$ consisting of nonzero scalar multiples of the identity transformation (see Scalar transformation).